Baggage

Sang-geun works at an airport baggage claim, placing bags onto a circular conveyor belt so that they do not collide with one another. Every bag travels along a straight conveyor belt and then drops onto the circular belt. Sang-geun sets the speed of the straight belt so that the bags never collide.

He wants to fix the straight belt at a single speed and then step away for a moment. A sensor on the straight belt tells him the position of every bag. Write a program that finds the maximum speed of the straight belt for which no two bags collide.

The circular belt has length $L$ and moves at $1\text{ m/s}$. At the instant a bag drops onto the circular belt, it collides with any other bag that lies within $1\text{ m}$ of it along the belt (a distance of exactly $1\text{ m}$ does not count as a collision). Because the belt is circular, distances wrap around its length $L$. People may take bags off the belt, but since it is impossible to know which bags they take, assume that no bag is ever removed. The straight belt can run at any speed between $0.1\text{ m/s}$ and $10\text{ m/s}$.

The first line contains the number of bags $N$ and the length of the circular belt $L$ ($1 \le N \le L \le 1000$). The second line contains the positions $x_i$ of the bags in meters ($0 \le x_i \le 1000$). Each $x_i$ is given with exactly two digits after the decimal point.

Print the maximum speed of the straight belt for which no bags collide, written as a reduced fraction. That is, express the maximum speed as an irreducible fraction $\dfrac{p}{q}$: if the denominator $q$ equals $1$, print only the integer $p$; otherwise print it in the form p/q. If no collision-free speed exists, print no fika.